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you

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so my name is Alex pixel I'm a graduate

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student at the University of Arizona

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I work in Daniel up high in his and

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other solar system work that's a project

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funded by NASA exoplanet Nexus program

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and today I'm going to be talking about

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the bulk properties of Proxima Centuri

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so some background and the month since

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the discovery we've seen a lot of really

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in depth and really insightful work done

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to treat this planet's atmosphere and

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potential habitability orbital evolution

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and even as we've seen the

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prospects for a characterization in the

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near future and I'm sure we're going to

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hear a lot more about that today but

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what I want to talk about and it's a lot

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along the slides of what Steven Kage's

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talked about is

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what underlying assumptions do we have

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here about the planets bulk properties

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in particular I want to know what can we

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observe and what can we not

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observational II constrain so we can

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observe stellar properties and many of

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the orbital properties but we don't know

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the inclination and so as we've heard

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when you measure an RV signal you're

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only given the mass projected along

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basically your line of sight what we

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cannot directly observe is a rocky or

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terrestrial composition we can't

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directly determine what the mass is and

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we really don't have much of a

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constraint observational e on what the

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radius might be I'm particularly

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concerned about the composition here

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there's been a growing consensus of sort

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of bimodal distribution from one to four

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Earth radii where you have of course

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planets like the earth small radius

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higher density but also larger planets

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with higher volatile on ice fractions

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similar in composition to but not

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necessarily as large as Neptune and of

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course that would have serious

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implications for the habitability which

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brings effect to the scene of this

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session

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so my general method is to place the

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observational constraints that we do

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have into a Bayesian framework where I

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substitute the non directly observable

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parameters with statistical priors based

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on previous work from planets for which

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for example we have combined transit and

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RD mass measurements for TGV mass

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it there we go occurrence rates from

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Kepler for the radius mass radius

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relationship to determine the mass we

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don't really have any observational

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constraints on the inclination I've

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assumed an isotropic distribution and

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then we have composition as a function

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of radius so I reference a pretty highly

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cited work by Leslie Rogers in 2015 who

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found that above about 1.6 or 3-day you

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see a sharp drop-off in the number of

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planets which are dense enough to be

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explained by a rocky composition

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so we feed all these priors in the

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observables into a Monte Carlo

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simulation from which we can extract

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posterior constraints on the mass the

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radius and the composition which are not

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directly observable

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so all directorates into the right panel

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here this represents a posterior mass

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distribution for the actual mass

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approximate Cindy I decomposed it into a

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blue shaded region representing a rocky

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population in the red shaded region

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representing a I call it a sub Neptune

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population but basically with a large

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volatile component or perhaps ice

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fraction and of course we see that the

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Iraqi population dominates the posterior

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mass distribution as we should expect

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for special Mass Planet

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we can extract from our parts terior

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distributions expectation values and to

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Sigma confidence intervals for the mass

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and radius

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briefly what I'll note here is of course

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the expectation value for the mass is a

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bit higher than the proposed measured a

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so-called minimum mass of which we would

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expect and also that the radius as I

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mentioned is not even with these

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constraints taken into place is not

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particularly well constrained but I

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thought that these values might be of

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use to

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in particular modelers who are trying to

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understand the interior composition of

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this planet we asked the question is the

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planet rocky we find that in our

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posterior distributions about 90% of the

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cases the planet does have a rocky

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composition bearing in mind that based

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on the scheme were using this work by

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Leslie Rogers in 2015 doesn't

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necessarily exclude very low radius

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population of volatile rich components

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so I put that as an upper bound but I

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imagine it's pretty close so these are

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the work this Buser results I published

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in February but what I'd like to do is

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expand upon this work for the more

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recent result from the California Kepler

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survey so we've seen a paper on the

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archive as of March I think which finds

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evidence for a dual peak distribution in

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the occurrence rates centered around

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about 1.75 Earth radii so this very

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straightforwardly lends itself to the

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interpretation that I've been discussing

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which is that we have a low radius more

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rocky population in a higher radius

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volatile population in fact if you were

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here on Tuesday there is a talk by Owen

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labour who presented a hydrogen manacle

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model a formulation which predicted that

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plaintiffs below 1.7 or three-day would

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lose volatile atmospheres very early on

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in the life Channel to start so this is

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highly consistent with that if we just

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take this as a hard boundary at 1.75 we

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had somewhat higher kin estimates for

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the expectation values for its mass and

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radius and I think a much better

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constraint on the probability that it's

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actually a rocky planet as originally

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proposed in the discovery paper that's

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about 95 percent so I'll discuss the

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significance of these results so for

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this target in particular I think we can

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all agree this is one of the most

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interesting targets we have I've

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provided more robust constraints on the

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mass radius and Composition the more

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originally available following discovery

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in particular I've calculated that it's

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about 95 percent likely that this planet

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does in fact have a composition

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comparable to that of the earth of

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then there's that one in 20 case and I

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think that becomes that it could

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actually have a volatile component I

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think that becomes important when you

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start expanding if we are able to push

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down our V sensitivity and find more and

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more small sized exoplanets in the

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what I have here is a plot of the chance

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that this planet is going to be rocky as

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a function of the measured in times of

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sine the inclination assuming all the

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other parameters stay about the same and

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what we see of course is that it falls

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off with increasing maps but also that

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it seems to be highly sensitive to where

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we draw this cutoff in our planet

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populations in your current rates to

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which radius does this transition

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so yeah in particularly basically this I

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want to know what I want to know is what

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are the underlying populations here what

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do these constituent populations look

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like in a function of occurrence versus

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radius it turns out if you have some

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pollution of the sub Neptune population

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to lower radii maybe 0.1 0.2 it doesn't

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significantly impact the results we

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could imagine that there's a very long

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tail here that which could extend all

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the way down to about north radius and

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could significantly increase the

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likelihood that we have the sub neptune

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masquerading as a 1.3 earth-mass planet

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I

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also think it's important to understand

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the spread in the mass radius

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relationship I borrowed this figure from

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the Weiss and Marci paper in 2014 but I

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can also provide an anecdote so in the

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past four weeks we discovered a rocky

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planet with a density all the 12 to 13

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grams per cubic centimeter around the M

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star in the habitable zone of LHS 1140 B

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we have also had seen updated masses for

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the Trappist one planets which assigns

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them densities which are consistent with

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a very significant water fraction 50

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percentile under person and so these are

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very similar systems and that they're

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both in stars they're both receiving

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about the same amount of insulation and

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yet we have such a large spread what

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these compositions can be and that

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provides us a lot of uncertainty and

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what the radius is if we can't measure

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it directly

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in general I think that we could apply

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this method to say directly imaged

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exoplanets if you know what planet this

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is you know it's not a rocky planet but

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we could imagine that we had seen

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something like this and we only have an

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idea of what the luminosity is that's a

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function of the radius as well as the

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albedo in the solar system even among

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solar system rocky planets albedo is

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highly unconstrained and so if we could

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get some sort of modeling prior

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constraints on what the albedo of a

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rocky planet is or volatile which planet

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is or colors photometric colors as well

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that can bind to the spectra would give

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us a much better idea of what kinds of

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targets targets were actually looking at

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with missions like Oh James goad would

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mainly have X blue bar

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so in conclusion I provided two sigma or

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95% confidence interval constraints on

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the mass and radius of this planet

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I've also provided an estimate of just

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how likely it is at this point in fact

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rocky and I think it's fairly high but

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of course because there's such a high

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mass tale and a potential for low mass

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vault average planets it's not one I

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think we need to do further work in

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particular to understand the underlying

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distribution of

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sub Neptune's versus rocky sized planets

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in radius space and to understand what

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causes the spread of the mass radius

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relationship can we control for factors

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such as stellar type or luminosity and

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finally I would generally encourage a

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more

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large-scale statistical approach to

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interpreting our results when we have

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planets with unobservable parameters

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namely our V detected indirectly image

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all right thank you Alex I so yes we

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have plenty time for questions okay

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Washington

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I love the talk I love your last

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sentence I'm a big fan of Bayesian

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statistics I just want to echo what I

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said earlier that in the case when we

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don't have data like for this planet

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like we don't know what it's true mass

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is and we have very little directly

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observed properties we want to use as

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many of the priors that we have

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available as possible and so it'd be

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awesome if we did combine the geometric

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probability with the studies that you

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showed up mass radius relations with the

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information that M dwarfs don't have

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giant planets look at actual the

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actually the distribution of planet

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population as a function of stellar mass

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and incorporate that into a Bayesian

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framework I imagine this would give you

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even stronger constraints on the

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probability that it's rocky oh

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right so these are the occurrence rates

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that you use for reference and right I

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haven't really thought specifically in

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terms of what populations appear around

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endorsing I think that would be

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important but I do at least try to

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constrain the occurrence rates of radii

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that's awesome I must have missed it

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slightly ya know it could be that some

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this graph and it's about one to one but

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this is not for any stars right right so

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of course that's something important to

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any more questions

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all right well if not let's thank Alex